Since a variety of problems corresponding to the real world nonlinear
phenomena can be transformed into fixed point problems (FPP). Therefore, it
is natural to study FPP associated with a class of mappings in a suitable
nonlinear framework. The term nonlinear framework for FPT is referred as a
metric space embedded with a "convex structure". It is remarked that the
non-positively curved hyperbolic space, introduced by Kohlenbach [1]}, provides rich geometrical structures suitable for MFPT of
various classes of mappings. For the results concerning MFPT in Kohlenbach
hyperbolic spaces, see, for example, , [2]}, [3]}, [4]}, [5]}, [6]}, [7]}
and the references cited therein. We are, therefore, interested into
iterative construction of fixed points of the class of quasi contractive
mappings in Kohlenbach hyperbolic spaces. As a consequence, we establish
results concerning rates of convergence associated with the modified Mann,
Ishikawa and Xu-Noor iterative algorithms, involving the class of quasi
contractive mappings, in comparison to the classical Picard iterative
algorithm in Kohlenbach hyperbolic spaces.
